Gravitation - Quick Revision
Kepler's laws
- Orbits: ellipses, Sun at one focus. 2. Areas: equal areas in equal times (= angular momentum conservation; slower at aphelion). 3. Periods: T^2 proportional to a^3.
Newton's law
- F = G m1 m2 / r^2 (attractive). G = 6.67e-11 N m^2/kg^2 (Cavendish). Shell: zero force inside, acts as point mass at centre for outside.
- g = GME/RE^2 (independent of body mass). Variation: altitude g~g(1-2h/RE); depth g=g(1-d/RE); g max at surface, zero at centre.
Energy & satellites
- Gravitational PE U = -GMm/r; potential V = -GM/r (both negative, zero at infinity). mgh is a near-surface approximation.
- Escape speed v_e = sqrt(2GME/RE) = sqrt(2gRE) ~ 11.2 km/s (independent of body mass/direction). Moon's ~2.3 km/s => no atmosphere.
- Orbital speed v_o = sqrt(GME/(RE+h)) (~7.9 km/s near surface; v_e = sqrt(2) v_o). Energy E = -GMEm/2(RE+h) = -KE (negative => bound). Weightlessness = free fall. Gravity cannot be shielded.